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JEE Main202127 Jul 2021Evening ShiftPhysicsMotion in One DimensionActual

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation F = F 0 1 - t - T T 2 where F 0 and T are constants. The force acts only for the time interval 2 T . The velocity v of the particle after time 2 T is:

Options

  1. A2   F 0   T M
  2. BF 0   T 2 M
  3. C4   F 0   T 3 M
  4. DF 0   T 3 M

Correct answer

C. 4   F 0   T 3 M

Step-by-step solution

t = 0 ,   u = 0 a = F o M - F o M T 2 ( t - T ) 2 = d v d t ∫ 0 v d v = ∫ t = 0 2   T F o M - F o M T 2 ( t - T ) 2 d t V = F o M t o 2   T - F o M T 2 t 3 3 - t 2   T + T 2 t 0 2   T V = 4   F o T 3 M

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